1. Introduction
Water quality monitoring plays an important role in many circumstances, such as tracking changes in water quality over time, identifying specific existing or emerging water quality problems, and periodically assessing water quality [
1,
2,
3]. Physical, chemical, and bacteriological analysis of water samples is crucial for water quality monitoring. Water sampling faces various challenges, including a lack of personnel, limited access to water bodies, and time constraints, particularly during natural disasters and emergencies. In addition, the quality of water samples significantly influences the analysis results. Depending on the analysis, the delivery time of water samples to a laboratory is also important. Ideally, within a few hours of collection, all water samples should be delivered to a central or regional laboratory [
4]. However, this situation depends on the security of vehicles for sampling officers and the quality of the transportation system. But these services are not widely accessible in many regions and countries. To address these issues, intelligent equipment and advanced technologies have been developed for autonomous water sampling from water bodies.
In recent years, UAMs have attracted great attention in academia and industry. They can offer aerial platforms (e.g., multirotors and helicopters) [
5] equipped with a wide range of robotic manipulators capable of physically interacting with the surroundings, which has expanded the capability of active operations for unmanned aerial vehicles. To this date, UAMs can execute some tasks where human access is restricted, such as aerial operation and grasp [
6], inspection and maintenance [
7], collaboration with ground robots [
8], transportation and position [
9], and canopy sampling [
10]. Motivated by this, UAMs can also be used for water sampling, especially around drain outlets, to ensure the reality of the water sample. As a complex robotic system, UAMs developed for water sampling face several significant challenges, such as structural design, system modeling, and motion control.
UAMs are complex multibody systems exhibiting coupled dynamic behavior, which should be considered in the design of their components. Kondak et al. [
11] developed an aerial manipulator with a total weight of 120 kg, composed of an autonomous helicopter and a seven-degree-of-freedom (DOF) industrial manipulator. The overweight can adversely affect the mission performance regarding payload capacity, working range, and control disturbances. Jimenez-Cano et al. [
12] chose a large-size helicopter as a platform to equip a heavy, multilink robotic arm. Designing an aerial manipulator system involves balancing the trade-offs between aerial mobility and manipulation capabilities, as well as considering factors such as power consumption, payload capacity, and control system stability. For the common low-price drones with weak load capacity, lightweight features play a critical role in aerial manipulator design. However, an apparent common shortcoming in the mentioned applications is that UAMs use high-weight robotic manipulators to perform tasks, but flight time is strictly shortened. The drive components of conventional unmanned aerial manipulators are mounted at the joints, resulting in high inertia and stiffness [
13,
14,
15]. A cable-driven mechanism has been integrated into unmanned aerial manipulators to cope with the above problems. The mechanism offers less inertia, higher flexibility, and better safety for operating objects by rearranging drive components and utilizing flexible cables to convey motion and force. The novel kind of prototype is commonly called a cable-driven aerial manipulator. Furthermore, a UAM with a light cable-driven manipulator will be designed for water quality sampling in this paper.
The first challenge in UAM research is dynamics modeling. The modeling methods of UAMs contain integral modeling and independent modeling [
16]. In integral modeling, the motion of each rigid body of the system is represented by the motion of a multilinked rigid body with a floating base, which is first studied in the field of space manipulators. For such complex dynamics modeling, Euler–Lagrange equations are mostly used, and the complete rigid body dynamics model obtained is very complex and computationally intensive. For example, Abaunza et al. developed a UAM with a 2-DOF manipulator, and derived the kinematic and dynamical equations of the whole system by combining the Newton–Euler method [
17]. Tomasz et al. used the Lagrangian method to obtain the analytical solutions of the generalized forces and moments of a UAM, and obtained dynamical models [
18]. The integral modeling approach ignores the changes in the center of gravity and inertia of the manipulator during operation, and directly considers the coupling terms as internal factors of the system, which can lead to a decrease in the accuracy of the modeling. The independent modeling approach treats the coupling effects between the aircraft and the manipulator as external disturbances, and models them separately [
19]. The dynamics model created by this method is not as complex as the holistic modeling approach, simplifying the modeling and control process. In our work, when the cable-driven aerial manipulator is in water sampling mode, the aircraft, in hover mode, is treated as a floating platform, and only the dynamics of the manipulator are considered. In flight mode, the manipulator serves as the payload of the aircraft, and only the dynamics of the aircraft are considered. Therefore, this paper intends to adopt an independent modeling method to obtain the system model of a UAM.
Another challenge for UAMs is controller design due to their complex dynamics. In some papers, the aircraft and manipulator are regarded as a single system for the purposes of control. A proportion integration differentiation (PID) controller was designed for a UAM to complete the grasping task [
20]. A decoupled adaptive controller based on Lyapunov theory was adopted to eliminate the effect produced by the manipulator of the UAM [
21]. Martin et al. proposed a variable-parameter integral inversion method to express the rotational inertia and center of mass of the aircraft as a function of the joint angle of the manipulator, and compensate for the motion of the aircraft in manipulator control [
22]. In addition, there are other control algorithms, such as feedback linearization [
23], the linear quadratic regulator control (LQR) algorithm [
24], fuzzy control [
25], nonlinear inverse control [
26], model predictive control [
27], and sliding mode control (SMC) [
28]. Among them, SMC is widely used in the control of electromechanical systems because of its strong robustness, simple structure, and insensitivity to parameters. However, the SMC structure contains switching functions, which cause the chattering phenomenon. Therefore, Ma et al. proposed the terminal sliding mode control (terminal SMC, TSMC) by adding higher-order nonlinear functions to the sliding mode surface, which effectively weakened the chattering, but it also posed discontinuity and singularity problems [
29]. Further, Yi et al. proposed a fast continuous nonsingular terminal sliding mode control strategy (fast nonsingular TSMC, FNTSMC) to solve the singularity problem and enhance the convergence of the system state [
30]. In addition, integral TSMC (ITSMC) can guarantee robustness by obtaining a suitable initial position so that the system has only a sliding phase, which provides a convergence in finite time and fast transient response [
31]. However, the lumped disturbances consisting of internal uncertainties and external perturbations existing in the cable-driven manipulator affect the steady-state performance of the joint variables, thus reducing the overall control quality of the system. According to the references [
32,
33], the state observer can effectively estimate and compensate for the lumped disturbances and improve the system’s resistance to disturbances. Among the state observers, the linear extended state observer (LESO) has the characteristics of low energy consumption and easy engineering implementations, and is successfully embedded in the structures of backstepping control (BC) [
34], adaptive control [
35], and PD (proportion differentiation, PD) control [
36]. Based on the analyses mentioned above, this paper intends to combine the advantages of ITSMC, BC, and LESO to design a motion controller for the cable-driven manipulator. Meanwhile, a disturbance observer (DOB) is introduced to estimate the disturbances of the aircraft, and the BC method is used to ensure the accuracy of the position and attitude of the aircraft.
A UAM for water sampling should be low-complexity, simple to operate, and effective from both a commercial and technical aspect. This paper focuses on the structural design, system modeling, and controller design of a UAM, all of which have research value and importance. The main contributions of this work are summarized as follows:
- (i)
We designed a flying robot equipped with a cable-driven aerial manipulator to collect water samples at the drain outlets. This design can effectively reduce the weight of the robotic arm and joint inertia, and improve the duty ratio of the end effector. As a result, our robotic arms are lightweight, dexterous, and capable of a fast response.
- (ii)
Compared with SMC schemes [
37,
38], a backstepping integral fast terminal sliding mode control based on the linear extended state observer (BIFTSMC-LESO) for the cable-driven manipulator is designed for the first time. The hybrid controller ensures that the state quantities can converge in finite time, and has better transient and steady-state performance.
- (iii)
Several practical factors, such as external disturbances, and internal unmodeled characteristics are considered in our work. We use DOB to observe the lumped disturbances for the quadrotor, and use the LESO to estimate the lumped disturbances for the manipulator, respectively. It can ensure stable tracking without information on the system compared with other controllers [
27,
39].
The rest of this paper is organized as follows.
Section 2 presents the mechanical design of the UAM. The system model is established in
Section 3.
Section 4 describes the controller design for the UAM.
Section 5 covers the simulation cases and results. The conclusions and suggestions for future work are shown in
Section 6.
2. Mechanical Design
The 3D virtual model of the developed UAM is shown in
Figure 1, which contains three main components, i.e., unmanned quadrotor, water sampling system, and cable-driven manipulator. The working principle of the prototype is to control the quadrotor to hover near the drain outlets, then manipulate the cable-driven manipulator to insert its end effector into the pipe mouth to collect water samples.
The aerial platform selected is an X450 quadrotor that has robust autonomous hovering capability with a minimum drift of position, and is well suited for positioning and navigational control strategies, which can increase the operational capability of the manipulator. It is equipped with a set of avionics, such as a flight controller, two pairs of motors and propellers, four electronic speed controllers, and a global position system (GPS). The GPS provides absolute positioning with respect to world coordinates, while inertial sensors provide required data for the attitude controller. In addition, the lithium battery, water pump, and water tank are placed in the aviation pods.
As illustrated in
Figure 2, the length of the fully extended robotic arm is 515 mm, the lengths of links 1 and 2 are 115 mm and 150 mm respectively, and the length of the end effector is 250 mm. The manipulator provides a light arm with cable-driven mechanisms that has two parallel joints. Each joint is driven by a DC geared motor installed in the aviation pods. A pair of driven cables (red and blue lines) are provided to control a joint rotating in two directions, which are kept under tension by the tension wheels. As a result, the joints can be controlled remotely through the driving wheels and guide wheels. Moreover, the manipulator also incorporates a suction pipe that draws water into the water tank installed in the aviation pods.
The cable-driven mechanism is described as follows by taking joint 2 as an example. As shown in
Figure 3, joint 2 is rotated clockwise by the red cable and counterclockwise by the blue cable. The torque produced by DC geared motor 2 is transmitted from driving wheel 2 to joint wheel 2 through the guide wheel. Starting at driving wheel 2, the red cable goes clockwise around driving wheel 2 before wrapping counterclockwise around guiding wheel 1. Afterwards, the red cable wraps around joint wheel 2 in a counterclockwise direction after going around two tension wheels in opposite directions. This completes the winding arrangement of a driving cable. As a result, joint 2 is driven clockwise by the red cable. Similarly, joint 2 rotates counterclockwise through the blue cable.
The inner structure of the aviation pods is shown in
Figure 4, which reveals the water collection mechanism. The water from the drain outlets is collected through the suction pipe, and flows into the water tank through the drain pipe. A water pump provides the power to ensure the wastewater can be pumped from lower levels to higher levels. The water pump is driven by a drive motor. The size of the water tank is 100 mm, which can hold about 1 L of wastewater.
3. System Modeling
Remark 1. The developed aerial manipulator is divided into two submodels, namely, a quadrotor model and a serial manipulator with two degrees of freedom. The coupling effect between the two submodels can be ignored during the modeling process, but treated as parametric uncertainties during controller design.
Three coordinate frames are used to describe the system: inertial coordinate frame {
I}, body coordinate frame {
B}, and manipulator coordinate frames {1}, {2}, and {
e}. Since the quadrotor is a rigid 6-DOF object, its dynamics can be computed by applying the Newton–Euler method. Here is the mathematical model for the quadrotor:
where
and
denote the position and attitude of the quadrotor, respectively. The term
is the inertia of the axes
x,
y, and
z, respectively. The term
is the drag coefficient and
is the aerodynamic friction factor,
m is the mass of the quadrotor, and
g is the gravitational acceleration.
is the control input, which satisfies the below relationship with the angular speeds
as follows:
where
and
are the thrust coefficient and torque coefficient, respectively.
L is the distance between the rotation axes and the center of the quadrotor.
Remark 2 ([
40])
. In this paper, the quadrotor takes flights near the hovering state. In this case, one observes that θ ≈ 0, ϕ ≈ 0, ≈ 0, ≈ 0, ≈ 1, ≈ 1. The yaw angle is not controlled frequently, so ≈ 0 can be obtained. Meanwhile, since the rotary inertia is small and the quadrotor is symmetric, one observes that ≈ . It should be noted that the linear model can describe a small range of flight modes, including hovering, low-speed flight, takeoff, and landing. Although there are some limitations, it can be used to describe the motion of the proposed aerial manipulator in this paper. Under Remark 2, the dynamic model (
1) can be simplified to the following form:
Assumption 1. For a cable-driven aerial manipulator, the motor transmits power to the joint along flexible cables so that the effect of the flexible cables can be equated with flexible joints. The flexibility of the joint is provided by a linear torsional spring system. Joint force and moment can be regarded as linearly related to joint flexibility variation.
Assumption 2. The joint flexibility also contains hysteresis, joint clearance, and other nonlinear factors.
Assumption 3. The motor rotors can be considered uniform cylinders.
With Assumptions 1–3, the dynamics model of the cable-driven aerial manipulator considering joint flexibility in non-contact mode is described as
where
,
,
,
,
, and
are the position, velocity, acceleration, inertia, damp, and input torque of the motors, respectively.
,
, and
are the position, velocity, and acceleration of the joints, respectively.
,
, and
are the inertia matrix, centrifugal and Coriolis forces term, and gravity term, respectively.
is the external disturbance.
Furthermore, we add the uncertain terms
,
, and
into Equation (
4), and the dynamics model can be rewritten as
where
is the system function that contains the internal unmodeled characteristics.
.
is the lumped disturbances.
6. Conclusions
In this paper, we developed a light cable-driven aerial manipulator for water sampling. Firstly, the proposed robot system was described and designed, including the quadrotor, manipulator, cable-driven mechanism, and other lightweight mechanical constructions. Then, the system model containing kinematics and dynamics of the UAM were established and analyzed, where the Newton–Euler method was adopted to model the position dynamics and attitude dynamics of the quadrotor, and the Lagrangian method was used to deduce the manipulator dynamics with flexible joints. Especially, the external disturbances and model uncertainty are considered in the system model. Furthermore, two controllers were developed to ensure the accurate operation for the UAM. The simulation results are summarized as follows. Firstly, the BC-DOB controller enables the quadrotor to maintain position and attitude stability, allowing it to achieve high trajectory tracking control accuracy. Secondly, the BIFTSMC-LESO controller can ensure greater overall performance than LADRC or the conventional SMC-ESO by increasing the convergence speed near the equilibrium point. Thirdly, the controller parameters can be tuned by an improved salp swarm algorithm, which ensures that the controllers have good transient performance and steady-state performance. Lastly, the proposed composite controller enables the UAM to perform the water sampling task better.
In the future, we will test the feasibility of the designed controller in a real environment. Further research will focus on other aerial tasks for the UAM, such as cooperative operation, aerial inspection, and grasping.